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H. L. Royden, “Real Analysis, Second Edition,” The Macmillan Company, New York, 1968.

has been cited by the following article:

• TITLE: Conditional Value-at-Risk for Random Immediate Reward Variables in Markov Decision Processes

  AUTHORS: Masayuki Kageyama, Takayuki Fujii, Koji Kanefuji, Hiroe Tsubaki

  KEYWORDS: Markov Decision Processes, Conditional Value-at-Risk, Risk Optimal Policy, Inventory Model

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.1 No.3, September 19, 2011

  ABSTRACT: We consider risk minimization problems for Markov decision processes. From a standpoint of making the risk of random reward variable at each time as small as possible, a risk measure is introduced using conditional value-at-risk for random immediate reward variables in Markov decision processes, under whose risk measure criteria the risk-optimal policies are characterized by the optimality equations for the discounted or average case. As an application, the inventory models are considered.